Hydrodynamic Source of the 11-year Solar Variations

Abstract

In the traditional axisymmetric models of the 11-year solar cycle, oscillations of the magnetic fields appear in the background of nonoscillating (over time scale considered) turbulent velocity fields and differential rotation. In this paper, an alternative approach is developed: The excitation of magnetic oscillations with the 22-year period is the consequence of hydrodynamic oscillations with the 11-year period. In the excitation of hydrodynamic oscillations, two processes taking place in high latitudes near the interface between the convective and radiative zones play a key role. One is forcing of the westerly zonal flow, the conditions for which are due to deformation of the interfacial surface. The other process is the excitation of a shear instability of zonal flow as a consequence of a strong radial gradient of angular velocity. The development of a shear instability at some stage brings about the disruption of the forcing of differential rotation. In the first (hydrodynamic) part of the paper, the dynamics of axisymmetric flows near the bottom of the convection zone is numerically simulated. Forcing of differential rotation having velocity shear in latitude and the existence of solutions in the form of torsional waves with the 11-year oscillation period are shown. In the second part the dynamics of the magnetic field is studied. The most pronounced peculiarities of the solutions are the existence of forced oscillations with the 22-year period and the drift of the toroidal magnetic field component from the mid latitudes to the equator. In high and low latitudes after cycle maximum, the toroidal component is of opposite sign in accordance with observations. In the third part, the transport of momentum from the bottom of the convection zone to the outer surface by virtue of diffusivity is considered. The existence of some sources of differential rotation in the convection zone is not implied. A qualitative correspondence of the differential rotation profile in the bulk of the convection zone and on its outer surface to experimental data is shown. The time correspondence between torsional and magnetic oscillations is also in accordance with observations.